Method and apparatus for determining orientation using a plurality of angular rate sensors and accelerometers

A method for determining the orientation of an object relative to a geographical coordinate system, comprising:

• providing a rotating sensor array with the precise rotational position relative to a local coordinate system and a precise rotational rate relative to the local coordinate system being known;
• using sensor data from the rotating sensor array to produce an overdetermined system of equations that can be solved for the unknown direction of the Earth rotation vector {circumflex over (ω)};
• solving, with a measure of the gravity vector ĝ, a rotation quaternion describing the orientation of the apparatus in the local coordinate system;
• and
• using values of ĝ and {circumflex over (ω)}, measured in the local coordinate system to compute a rotation quaternion required to rotate the local coordinate system into the geographical coordinate system.